📝 Exam Questions — Physics

The quality of a measurement is often described in terms of its precision and accuracy, which are influenced by the instrument used. (a) Describe how the precision of an instrument relates to the number of significant figures in a measurement. [4] (b) Suggest an appropriate instrument to measure a time interval of approximately 0.5 s with high precision. [3]

All derived units can be expressed in terms of the seven SI base units. This process helps in checking the homogeneity of physical equations. (a) Show that the SI base units of force (newton) are kg m s⁻². [4] (b) Determine the SI base units of power, given that power is the rate of doing work. [4]

Physical quantities are often expressed using prefixes to denote multiples or submultiples of SI units. (a) Describe the general rules for using prefixes with SI units, such as kilo- or micro-. [4] (b) Illustrate how ambiguity can arise if a capital 'M' is used for 'milli' instead of 'mega' and give an example. [4]

In an experiment to measure the period of oscillation of a simple pendulum, a student uses a stopwatch. (a) Identify three common sources of random errors in an experiment involving the measurement of time. [3] (b) Describe how taking multiple readings and calculating an average can reduce the effect of random errors. [4]

A student investigates the relationship between voltage V and current I for a resistive component. The student records the following data:

The absolute uncertainty in current is negligible. (a) Plot a graph of V (y-axis) against I (x-axis), including error bars for voltage. [4] (b) Determine the gradient of the graph and its absolute uncertainty. [4] (c) Calculate the percentage uncertainty in the resistance, R, using the gradient from (b), given R = V/I. [4]

A student performs an experiment to measure the mass of a known standard mass. The known mass is 10.00 g. The student records five measurements using a digital balance. (a) Analyse the following five measurements: 9.95 g, 9.97 g, 9.96 g, 9.94 g, 9.98 g. Comment on the accuracy and precision of these measurements. [6] (b) Suggest two ways to improve both the accuracy and precision of these measurements. [4]

A student needs to measure the length of a classroom desk for an experiment. They have access to both a metre rule and a digital Vernier caliper. (a) Compare the suitability of using a metre rule versus a digital Vernier caliper for measuring the length of the desk, considering aspects of accuracy and precision. [6] (b) Evaluate the impact of choosing an instrument with insufficient precision on the overall uncertainty of an experiment, giving an example. [5]

Understanding the fundamental units of physical quantities is essential for checking the consistency of equations. (a) Determine the base units of force. [3] (b) The derived unit of power is the Watt (W). Show that the derived unit of power can be expressed in base units as kg m² s⁻³. [5]

In scientific communication, it is important to follow standard conventions for writing symbols and units. (a) State the correct symbol for the unit 'second'. [2] (b) Correct the following incorrect unit notation: '30 mS' if it refers to 30 metres. [2]

Fig 1.1 shows a graph of current (I) against voltage (V) for a resistor. (a) Analyse the unit conventions used on the axes in Fig 1.1 and identify any potential ambiguities if the units were not clearly labelled. [6] (b) Sketch a similar graph for a filament lamp, ensuring correct labelling of axes with appropriate symbols and units, following SI conventions. [5]

A student is carrying out an experiment involving a length of wire and a spherical object. (a) Determine the absolute uncertainty in the length of a wire if its measured length is 120.0 ± 0.2 cm. [3] (b) Calculate the percentage uncertainty in the volume of a sphere with radius r = 3.50 ± 0.05 cm. The formula for the volume of a sphere is V = (4/3)πr^3. [6]

A student measures the dimensions of a rectangle. The length L is measured as 15.0 ± 0.1 cm and the width W is measured as 5.0 ± 0.2 cm. (a) Calculate the absolute uncertainty in the area of the rectangle. [5] (b) Compare the percentage uncertainty in the length and the width, and comment on which contributes more to the overall uncertainty in the area. [4]

A student is analysing different forces acting on an object. (a) Identify which of the forces shown is a vector quantity. [2] (b) Explain what information, besides magnitude, is conveyed by a vector quantity. [2] (c) Sketch a diagram showing the resultant force of two perpendicular forces, 3 N acting horizontally and 4 N acting vertically. [3]

Orders of magnitude are useful for making quick estimations and comparing very different scales in physics. (a) Estimate the order of magnitude of the time it takes for light to travel across a typical classroom (approximately 10 m). [3] (b) Calculate the order of magnitude of the volume of a human head, assuming it is roughly spherical with a radius of 10 cm. Show your working. [4]

When conducting experiments, it is crucial to understand the nature of errors that can affect measurements. (a) Describe the difference between a systematic error and a random error. [4] (b) Suggest how a systematic error can be identified and reduced in an experiment to measure the period of a pendulum. [4]

Fig. 1.1 shows an experimental setup for measuring the period of a simple pendulum. (a) Identify a possible systematic error in the setup shown in Fig. 1.1. [2] (b) Explain how this systematic error would affect the measured value. [3] (c) Suggest a method to reduce the effect of this systematic error. [3]

A student determines the density of a metal block in the laboratory. (a) Calculate the percentage uncertainty in the density of a metal block if its mass is measured as 250 ± 5 g and its volume is measured as 30.0 ± 0.5 cm^3. [6] (b) Discuss which measurement (mass or volume) contributes more significantly to the overall percentage uncertainty in the density. [4]

Standard conventions for symbols and units are crucial in physics. (a) Explain why it is important to follow standard conventions for symbols and units in scientific communication. [4] (b) Give two examples of common errors in writing unit symbols and their correct forms. [3]

Fig. 1.1 shows a target board with several bullet holes, representing a set of measurements. The bullseye indicates the true value of the quantity being measured. (a) Interpret the distribution of the data points shown in Fig. 1.1 in terms of precision. [4] (b) Evaluate whether the measurements are accurate, given that the true value is indicated by the bullseye. [4]

The Système Internationale (SI) defines a set of base units from which all other units are derived. (a) State two base SI units. [2] (b) Define what is meant by a derived unit and give one example. [3]

Fig. 3.1 shows a simple pendulum setup, with a mass suspended by a string from a clamp stand. The pendulum is shown oscillating. (a) Estimate the order of magnitude of the length of the pendulum in Fig. 3.1, given its period is approximately 2 seconds. [3] (b) Compare this estimated length with the order of magnitude of the height of a typical laboratory bench. [3] (c) Suggest why understanding orders of magnitude is important when designing experiments like the one shown. [3]

The SI system provides a coherent set of units. Some quantities have their own special names for their derived units. (a) Identify two derived quantities. [2] (b) Express the unit of energy, the Joule (J), in terms of base SI units. [4]

Orders of magnitude provide a quick way to estimate the size of physical quantities without needing precise measurements. (a) State the order of magnitude of the typical height of an adult human in metres. [2] (b) State the order of magnitude of the typical mass of an apple in kilograms. [2]

In experimental physics, it is crucial to understand the difference between accuracy and precision when evaluating measurements. (a) Explain how systematic errors affect the accuracy of a measurement. [4] (b) State how random errors affect the precision of a measurement. [3]

A student is conducting an experiment to measure the resistance of a wire using a voltmeter and an ammeter. (a) Discuss the difference between systematic errors and random errors, giving an example of each in the context of measuring the resistance of a wire. [6] (b) Suggest methods to minimise the impact of both systematic and random errors in the resistance measurement. [4]

The power P dissipated in a resistor is given by the formula P = I²R, where I is the current and R is the resistance. The current I is measured as (2.00 ± 0.04) A and the resistance R is measured as (50.0 ± 1.5) Ω. (a) Show that the fractional uncertainty in the power P is given by (ΔR/R) + 2(ΔI/I). [4] (b) Calculate the percentage uncertainty in the power P. [4]

The Système Internationale (SI) defines a set of base units from which all other derived units are formed. This system is widely adopted in scientific and engineering fields globally. (a) Discuss the advantages of using a single, coherent system of units like the SI system in science and engineering. [5] (b) Explain why the mole and the candela are considered base units, despite not being directly related to everyday mechanical or electrical phenomena. [5]

A car's performance is often described using different units for speed and pressure. (a) A car travels at a speed of 30 m/s. Calculate its speed in km/h. [3] (b) A pressure of 2.0 × 10⁵ Pa is exerted on a surface. Determine the base units of pressure. [4]

A student measures the mass of a beaker as (150.0 ± 0.5) g and then adds some liquid, measuring the mass of the beaker and liquid as (280.5 ± 0.5) g. (a) Calculate the absolute uncertainty in the total mass of the liquid. [4] (b) Determine the percentage uncertainty in the total mass of the liquid, expressing your answer to an appropriate number of significant figures. [4]

Physical quantities are fundamental to the description and understanding of the physical world. (a) Distinguish between a scalar quantity and a vector quantity, providing an example for each. [4] (b) Give three examples of physical quantities that are fundamental in physics. [3]

The Système Internationale (SI) defines a set of base quantities and their corresponding base units, which form the foundation of all physical measurements. (a) Name the three SI base quantities associated with mechanics and their corresponding base units. [3] (b) State the SI base unit for electric current and for thermodynamic temperature. [3]

Physics involves the measurement of various aspects of the physical world. (a) Define what is meant by a physical quantity. [2] (b) State three examples of physical quantities that are not base quantities. [3]

Dimensional analysis is a powerful tool for verifying physical relationships. (a) The period T of a simple pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration of free fall. Determine the base units of both sides of the equation to show it is homogeneous. [6] (b) Discuss the limitations of using dimensional analysis to derive or check physical equations. [4]

When measuring physical quantities in an experiment, it is crucial to understand the types of errors that can occur. (a) Outline what is meant by a zero error. [3] (b) Draw a sketch of a protractor scale that exhibits a positive zero error. [3]

An experiment is conducted to measure a constant voltage over a period of time. The results are plotted in Fig. 1.1. (a) Describe the pattern of the data points shown in Fig. 1.1 and relate it to the presence of random errors. [4] (b) Explain how taking multiple readings and calculating an average can reduce the impact of random errors. [3]

Fig. 4.1 shows a simple series electrical circuit containing a power supply, a resistor, an ammeter connected in series, and a voltmeter connected in parallel across the resistor. (a) Identify the SI base units for the resistance R in Fig. 4.1. [2] (b) Explain how the SI base units of resistance can be derived from Ohm's Law (V=IR) and the definition of power (P=VI). [3] (c) Calculate the resistance of the resistor shown, given the voltmeter reading is 6.0 V and the ammeter reading is 2.0 A, and state its units in terms of SI base units. [4]

A student measures the length of an object using a ruler. (a) State the absolute uncertainty for a measurement of 2.50 cm taken with a ruler graduated in millimetres. [2] (b) Calculate the percentage uncertainty for this measurement. [2]

In experimental physics, understanding the types of errors that can affect measurements is important for data analysis. (a) Define the term 'random error'. [2] (b) Give one example of a random error in an experiment measuring the period of a pendulum. [2]

Orders of magnitude are a powerful tool in physics for conceptual understanding and problem-solving, especially when dealing with quantities that span vast scales. (a) Discuss the utility of using orders of magnitude in physics, particularly when dealing with extremely large or small quantities. [5] (b) Compare the order of magnitude of the mass of an electron (approximately 9.11 x 10⁻³¹ kg) with the order of magnitude of the mass of a proton (approximately 1.67 x 10⁻²⁷ kg). [5]

Fig. 1.1 shows an ammeter with an analogue scale. Before any current is applied, the needle rests at 0.1 A. (a) Identify the type of error that is evident in the readings from Fig. 1.1. [2] (b) Explain how this type of error affects the accuracy of the measurements. [2] (c) Suggest one way to eliminate or reduce this error. [2]

The study of physics relies on precise measurements and clear communication of concepts. (a) Discuss the importance of defining physical quantities clearly in scientific communication. [5] (b) Explain why some physical quantities are considered 'derived' while others are 'base' quantities. [5]

Physical equations must be dimensionally consistent to be valid. (a) Show that the equation for kinetic energy, E_k = 1/2 mv², is homogeneous with respect to its base units. [5] (b) Explain why checking for homogeneity does not guarantee an equation is physically correct. [2]

When performing experiments, the selection of appropriate measuring instruments is crucial for obtaining reliable data. (a) Identify two factors that influence the choice of instrument for a measurement. [2] (b) State an appropriate instrument for measuring the diameter of a thin wire and explain why it is suitable. [3]

A student investigates the speed of waves on a stretched string. They propose an equation relating the wave speed to other physical quantities. (a) A student proposes an equation for the speed of waves on a string as v = √(T/μ), where T is the tension in the string and μ is the mass per unit length. Evaluate the homogeneity of this equation using base units. [8] (b) If the equation were proposed as v = T/μ, determine whether it would be homogeneous. Show your working. [4]

In experimental physics, it is important to understand different types of errors. (a) Define what is meant by a random error. [2] (b) Give three examples of random errors that might occur in a laboratory experiment. [3]

Fig 1.1 shows a section of a ruler with markings. When measuring small lengths, prefixes are often used with SI units. (a) Interpret the meaning of the prefix 'μ' in the context of units from Fig 1.1. [3] (b) A student measures a length and records it as '2.5 mm'. Suggest why this notation is preferred over '0.0025 m' in certain contexts and explain the convention for writing units with prefixes. [6]

In experimental physics, it is important to understand the quality of measurements. (a) Distinguish between accuracy and precision in scientific measurements. [3] (b) Give an example of a measurement that is precise but not accurate. [2]

Dimensional analysis is used to verify the consistency of physical equations. (a) Analyse the homogeneity of the equation P = Fv, where P is power, F is force, and v is velocity, by expressing all terms in base units. [5] (b) Deduce the base units for the constant 'k' in the equation F = kx, where F is force and x is extension. [3]

A block of mass 2.0 kg rests on an inclined plane at an angle of 30° to the horizontal. (a) Draw a labelled diagram showing the weight and the normal contact force acting on the block, resolved into components parallel and perpendicular to the incline. [3] (b) Calculate the component of the weight acting parallel to the incline. [4] (c) Discuss how the normal contact force changes as the angle of inclination increases. [3]

An airplane experiences a lift force of 200 kN acting at an angle of 10° from the vertical, directed towards the front of the plane, as shown in Fig 1.1. (a) Calculate the vertical component of the lift force. [4] (b) Determine the horizontal component of the lift force. [3]

When multiple forces act on an object, their combined effect can be represented by a single vector. (a) State the meaning of the term 'resultant vector'. [2] (b) Describe the head-to-tail method for adding two vectors graphically. [4]

A student pulls a sled across a flat, snowy field. The student applies a force of 150 N to the sled using a rope, held at an angle of 30° above the horizontal. (a) Calculate the magnitude of the horizontal force component applied by the student. [4] (b) Determine the magnitude of the vertical force component applied by the student. [4]

In physics, quantities are classified as either scalar or vector, which impacts how they are used in calculations. (a) Distinguish between scalar and vector quantities. [3] (b) Explain why electric current is typically treated as a scalar quantity, despite having a direction. [4]

A block of mass m is being pulled up an inclined plane by a force F acting parallel to the incline, as shown in Fig 1.2. The incline makes an angle θ with the horizontal. There is a coefficient of kinetic friction μ between the block and the plane, and the block moves at a constant velocity. (a) Derive an expression for the magnitude of the force F required to pull the block up the incline at constant velocity, in terms of its mass m, the angle of inclination θ, the coefficient of kinetic friction μ, and the acceleration of free fall g. [4] (b) Explain the significance of resolving the weight and the normal force into components when dealing with inclined planes. [4] (c) Calculate the force F if m = 5.0 kg, θ = 30 degrees, and μ = 0.20. (Take g = 9.81 m s⁻²) [4]

A force is an example of a vector quantity that can be resolved into components. (a) Draw a diagram representing a force of 60 N acting at an angle of 30° to the horizontal. Label the force and the angle clearly. [4] (b) Calculate the horizontal and vertical components of this force. [4]

Physical quantities can be categorised based on whether they have a direction associated with them. (a) Define a vector quantity. [2] (b) Give three examples of vector quantities. [3]

Understanding the fundamental properties of physical quantities is essential in physics. (a) Define a scalar quantity. [2] (b) Give three examples of scalar quantities. [3]

Vectors are used to represent physical quantities that have both magnitude and direction. (a) Describe how a vector quantity is typically represented diagrammatically. [2] (b) State two pieces of information conveyed by a vector arrow. [2]

A block is pulled across a horizontal surface by a rope, as shown in Fig 1.2. (a) Describe how resolving a vector into perpendicular components simplifies the analysis of its effects. [3] (b) The tension in the rope shown in Fig 1.2 is 120 N, and the rope makes an angle of 25° to the horizontal. Calculate the vertical component of the tension in the rope. [4]

An aircraft is flying at a constant velocity, but is subject to a crosswind. (a) The aircraft is flying North at 200 m s⁻¹ and there is a crosswind of 50 m s⁻¹ blowing East. Determine the magnitude and direction of the resultant velocity of the aircraft. [5] (b) Explain how the choice of method (graphical vs. component method) for vector addition might affect the accuracy and precision of the resultant, and compare their suitability for different scenarios. [6]

Two forces act perpendicularly on an object. (a) Calculate the magnitude of the resultant force when two perpendicular forces, 3.0 N and 4.0 N, act on an object. [4] (b) Determine the direction of the resultant force relative to the 3.0 N force. [4]

Forces and displacements are vector quantities. (a) Show, using a labelled vector diagram, how to find the resultant of two forces, F₁ and F₂, acting at an angle to each other. [4] (b) Calculate the resultant displacement of a person who walks 5.0 km East and then 12.0 km North. [4]

In navigation, the velocity of an object is often described using a bearing, which is an angle measured clockwise from North. (a) Sketch a vector representing a velocity of 25 m s⁻¹ at a bearing of 045° (measured clockwise from North). [4] (b) Discuss the importance of choosing an appropriate scale when representing vectors graphically, especially when dealing with multiple vectors of varying magnitudes. [6]

The process of splitting a single vector into two components is known as vector resolution. (a) Name the two trigonometric functions commonly used for resolving a vector into perpendicular components. [2] (b) Suggest a practical situation where resolving a force into components is necessary. [2]

Fig. 1.2 shows an object on a flat surface being pulled by two ropes. (a) Analyse the forces acting on an object being pulled by two ropes, as shown in Fig. 1.2. The first rope applies a force of 50 N at 30° to the horizontal, and the second rope applies a force of 70 N at 60° to the horizontal in the same plane. [6] (b) Deduce the magnitude and direction of the single force that would produce the same effect as these two forces. [6]

Vectors can be split into components to simplify analysis. (a) Define what is meant by the resolution of vectors. [2] (b) State the two conditions that must be met by the components of a resolved vector. [3]

The radius, r, of a sphere is measured as (2.50 ± 0.05) cm. The formula for the volume of a sphere is V = (4/3)πr³. (a) Calculate the percentage uncertainty in the volume of the sphere. [5] (b) Determine the absolute uncertainty in the calculated volume. [4]

Two forces, F₁ and F₂, act on an object as shown in Fig 1.1. Force F₁ has a magnitude of 100 N and acts at an angle of 30° above the horizontal. Force F₂ has a magnitude of 50 N and acts purely horizontally to the right. (a) Show that the magnitude of the resultant force acting horizontally is approximately 137 N. [4] (b) Determine the magnitude of the resultant force acting vertically. [4]

A hiker walks across varied terrain, moving from a starting point to a final destination. (a) Compare distance and displacement, identifying which is a scalar and which is a vector. [4] (b) Evaluate a situation where understanding the vector nature of a quantity (e.g., velocity) is critical, providing a practical example. [6]

A force of 30 N is applied to an object at an angle of 45 degrees to the horizontal, as shown in Fig 1.1. (a) Show that the horizontal component of the force is approximately 21.2 N. [3] (b) Calculate the vertical component of the force. [3]

A projectile is launched from the ground with an initial velocity of 25 m s⁻¹ at an angle of 40° above the horizontal. (a) Calculate the horizontal and vertical components of the velocity of the projectile at launch. [5] (b) Find the magnitude of the projectile's velocity after 1.0 s, assuming negligible air resistance. [4]

A block of weight W is suspended by two identical cables, each making an angle θ with the horizontal ceiling, as shown in Fig 1.2. (a) Derive an expression for the tension in each cable in terms of the block's weight W and the angle θ. [4] (b) Explain why the horizontal components of the tension must be equal and opposite. [3] (c) Evaluate the tension in each cable when the block's weight is 150 N and the angle θ is 45°. [4]

A student measures the mass (m), diameter (d), and height (h) of a solid cylindrical block to determine its density (ρ). The measurements are recorded as: Mass, m = 150.0 ± 0.5 g Diameter, d = 2.00 ± 0.02 cm Height, h = 5.00 ± 0.05 cm (a) Calculate the absolute uncertainty in the density of the cylinder. [6] (b) Evaluate which measurement (mass, diameter, or height) contributes most to the overall percentage uncertainty in the density. [4]

Fig 1.1 shows a force vector acting on an object. (a) Identify the horizontal and vertical components of the force shown in Fig 1.1. [2] (b) Calculate the magnitude of the horizontal component of the force. [4]